An analytic solution to the Busemann-Petty problem on sections of convex bodies

We derive a formula connecting the derivatives of parallel section functions of an origin-symmetric star body in R^n with the Fourier transform of powers of the radial function of the body. A parallel section function (or (n-1)-dimensional X-ray) gives the ((n-1)-dimensional) volumes of all hyperplane sections of the body orthogonal to a given direction. This formula provides a new characterization of intersection bodies in R^n and leads to a unified analytic solution to the Busemann-Petty problem: Suppose that K and L are two origin-symmetric convex bodies in R^n such that the ((n-1)-dimensional) volume of each central hyperplane section of K is smaller than the volume of the corresponding section of L; is the (n-dimensional) volume of K smaller than the volume of L? In conjunction with earlier established connections between the Busemann-Petty problem, intersection bodies, and positive definite distributions, our formula shows that the answer to the problem depends on the behavior of the (n-2)-nd derivative of the parallel section functions. The affirmative answer to the Busemann-Petty problem for n\le 4 and the negative answer for n\ge 5 now follow from the fact that convexity controls the second derivatives, but does not control the derivatives of higher orders.Comment: 13 pages, published versio

Symmetrization in Geometry

The concept of an $i$-symmetrization is introduced, which provides a convenient framework for most of the familiar symmetrization processes on convex sets. Various properties of $i$-symmetrizations are introduced and the relations between them investigated. New expressions are provided for the Steiner and Minkowski symmetrals of a compact convex set which exhibit a dual relationship between them. Characterizations of Steiner, Minkowski and central symmetrization, in terms of natural properties that they enjoy, are given and examples are provided to show that none of the assumptions made can be dropped or significantly weakened. Other familiar symmetrizations, such as Schwarz symmetrization, are discussed and several new ones introduced.Comment: A chacterization of central symmetrization has been added and several typos have been corrected. This version has been accepted for publication on Advances in Mathematic

Vibrational intensity distributions for continuum photoionization of oxygen

Results from measurements of vibrational intensity distributions for continuum photoionization of O2 are reported. Measurements were made using the 584 and 304 A He lines. The photoionization cross section of O2 shows a substantial dip in magnitude over a 20 A band centered about 590 A; thus the possibility exists that a 584 A photoelectron spectrum of O2 includes an autoionized contribution and the vibrational intensity distributions may not correspond to those of continuum ionization. Oxygen photoionization cross section shows no structure around 304 A and purley continuum ionization is expected

On the ionization potential of molecular oxygen

The ionization potential of O2 was measured by the technique of high resolution photoelectron spectroscopy taking into account the influence of rotational structure on the shape of the vibrational bands. A value of 12.071 + or - .001 eV (1027.1 + or - 0.1 A) was found for the ionization potential. A lowering of the ionization potential caused by a branch-head when delta N = -2 gave an appearance potential for ionization of 12.068 + or - .001 eV (1027.4 + or - 0.1 A)

Collecting efficiency of a cylindrical mirror electron energy analyzer with preretarding lens

The electron collecting efficiency of a cylindrical mirror energy analyzer incorporating retardation of the electrons prior to analysis has been determined over the range 0 to 30 eV by two methods. The first method requires the use of a vacuum ultraviolet monochromator to produce monoenergetic electrons of different energies; the second method involves measuring the energy-brightness relationship of the retarding optics and should be applicable to any deflection analyzer with pre-retarding optics. The results of the two methods are compared and the limitations of the latter method are discussed

Independent Orbiter Assessment (IOA): Assessment of instrumental subsystem FMEA/CIL

The McDonnell Douglas Astronautics Company (MDAC) was selected in June 1986 to perform an Independent Orbiter Assessment (IOA) of the Failure Modes and Effects Analysis (FMEA) and Critical Items List (CIL). The IOA effort first completed an analysis of the Instrumentation hardware, generating draft failure modes and potential critical items. To preserve independence, this analysis was accomplished without reliance upon the results contained within the NASA FMEA/CIL documentation. The IOA results were then compared to the NASA FMEA/CIL baseline. A resolution of each discrepancy from the comparison is provided through additional analysis as required. The results of that comparison for the Orbiter Instrumentation hardware are documented. The IOA product for Instrumentation analysis consisted of 107 failure mode worksheets that resulted in 22 critical items being identified. Comparison was made to the Pre 51-L NASA baseline with 14 Post 51-L FMEAs added, which consists of 96 FMEAs and 18 CIL items. This comparison produced agreement on all but 25 FMEAs which caused differences in 5 CIL items

New Prospects in Fixed Target Searches for Dark Forces with the SeaQuest Experiment at Fermilab

An intense, 120 GeV proton beam incident on an extremely long, iron target generates enormous numbers of light-mass particles that also decay within that target. If one of these particles decays to a final state with a hidden gauge boson, or if such a particle is produced as a result of the initial collision, then that weakly interacting, hidden-sector particle may traverse the remainder of the target and be detected downstream through its possible decay to an $e^+e^-$, $\mu^+\mu^-$, or $\pi^+\pi^-$ final state. These conditions can be realized through an extension of the SeaQuest experiment at Fermilab, and in this initial investigation we consider how it can serve as an ultrasensitive probe of hidden vector gauge forces, both Abelian and non-Abelian. A light, weakly coupled hidden sector may well explain the dark matter established through astrophysical observations, and the proposed search can provide tangible evidence for its existence --- or, alternatively, constrain a "sea" of possibilities.Comment: 14 pages, 8 figures; improved sensitivity analysis and cross-checks; small shifts in the expected limits; conclusions unchanged; refs. adde

Evaluation of AIS Data for Agronomic and Rangeland Vegetation: Preliminary Results for August 1984 Flight over Nebraska Sandhills Agricultural Laboratory

Since 1978 scientists from the Center for Agricultural Meteorology and Climatology at the University of Nebraska have been conducting research at the Sandhills Agricultural Laboratory on the effects of water stress on crop growth, development and yield using remote sensing techniques. We have been working to develop techniques, both remote and ground-based, to monitor water stress, phenological development, leaf area, phytomass production and grain yields of corn, soybeans and sorghum. Because of the sandy soils and relatively low rainfall at the site it is an excellent location to study water stress without the necessity of installing expensive rainout shelters. The primary objectives of research with the airborne imaging spectrometer (AIS) data collected during an August 1984 flight over the Sandhills Agricultural Laboratory are to evaluate the potential of using AIS to: (1) discriminate crop type; (2) to detect subtle architectural differences that exist among different cultivars or hybrids of agronomic crops; (3) to detect and quantify, if possible, the level of water stress imposed on the crops; and (4) to evaluate leaf area and biomass differences for different crops